91Ó°ÊÓ

• The mass of a ball is$1.4kg$.

• The stiffness is$4N/m$

• The amplitude is $14cm$

• The strength of the gravitational field is only $1/6ofthatearth$

Stiffnessis defined asthe force required producing a unit deformation.

Amplitude is defined as the maximum displacement obtained by the object.

Angular Frequency is defined as the angular displacement of any object of the wave in unit time.

Angular Frequency,

$\mathit{Ó\neg }\mathbf{=}\sqrt{\frac{{\mathbf{k}}_{\mathbf{s}}}{\mathbf{m}}\mathbf{}\mathbf{}}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{\left(}\mathbf{1}\mathbf{\right)}$

where,

$$\begin{gathered} k_s=Thestiffness \\ m=Themass \end{gathered}$$

Substituting the values in above expression,

$$\begin{gathered} \mathrm{Ó\neg }=\sqrt{\frac{4}{1.4}} \\ \mathrm{Ó\neg }=2.86rad/s \end{gathered}$$

Hence, the angular frequency is$\mathbf{2}\mathbf{.}\mathbf{86}\mathbf{}\mathit{r}\mathit{a}\mathit{d}\mathbf{/}\mathit{s}$

Frequency is defined as the number of cycles required to complete a full wave per unit time.

Frequency,

$$\begin{gathered} \mathit{f}\mathbf{=}\frac{\mathbf{Ó\neg }}{\mathbf{2}\mathbf{Ï€}} \\ =\frac{2.86}{2\mathrm{Ï€}} \\ =0.45Hertz \end{gathered}$$

Hence, the frequency is $\mathbf{0}\mathbf{.}\mathbf{45}\mathbf{}\mathit{H}\mathit{e}\mathit{r}\mathit{t}\mathit{z}$.

Time Period is defined as the time required completing a full wave to cross a point.

Period,

$\mathit{T}\mathbf{=}\frac{\mathbf{2}\mathbf{Ï€}}{\mathbf{Ó\neg }}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{\left(}\mathbf{2}\mathbf{\right)}$

Substituting the value in above expression,

$$\begin{gathered} T=\frac{2\mathrm{Ï€}}{2.86} \\ T=2.2s \end{gathered}$$

Hence, the period is $\mathbf{2}\mathbf{.}\mathbf{2}\mathbf{}\mathit{s}$.

Time period of the Moon,

$$\begin{gathered} T_{moon}≈\sqrt{6.}{T}_{earth} \\ Where,T_{earth}=2.2s \\ {T}_{moon}≈\sqrt{6}×2.2s \\ ≈5.39s \end{gathered}$$

Hence, the time period of Moon is$\mathbf{5}\mathbf{.}\mathbf{39}\mathbf{}\mathit{s}$